Abstract
The well-known Marcinkiewicz-Zygmund inequality ∫ 0 2x |T(x)| pdx 1 p ⩽A p 1 n ∑ k=0 2n T 2kπ 2n+1 p 1 p , 1<p<+∞ , where T is a trigonometric polynomial of degree n and A p depends on p only, will be generalized to have the right hand side containing the derivative values as well. The results will then be applied to prove the mean convergence of the Hermite interpolation by trigonometric polynomials on equidistant nodes.
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